LMFDB - Embedded newform 112.4.i.c.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,4,Mod(65,112)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("112.65");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	112.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.60821392064$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	112.81
Dual form			112.4.i.c.65.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.50000 - 6.06218i) q^{3} +(-3.50000 - 6.06218i) q^{5} +(-14.0000 - 12.1244i) q^{7} +(-11.0000 - 19.0526i) q^{9} +(-2.50000 + 4.33013i) q^{11} -14.0000 q^{13} -49.0000 q^{15} +(10.5000 - 18.1865i) q^{17} +(24.5000 + 42.4352i) q^{19} +(-122.500 + 42.4352i) q^{21} +(-79.5000 - 137.698i) q^{23} +(38.0000 - 65.8179i) q^{25} +35.0000 q^{27} +58.0000 q^{29} +(73.5000 - 127.306i) q^{31} +(17.5000 + 30.3109i) q^{33} +(-24.5000 + 127.306i) q^{35} +(-109.500 - 189.660i) q^{37} +(-49.0000 + 84.8705i) q^{39} +350.000 q^{41} +124.000 q^{43} +(-77.0000 + 133.368i) q^{45} +(262.500 + 454.663i) q^{47} +(49.0000 + 339.482i) q^{49} +(-73.5000 - 127.306i) q^{51} +(-151.500 + 262.406i) q^{53} +35.0000 q^{55} +343.000 q^{57} +(-52.5000 + 90.9327i) q^{59} +(206.500 + 357.668i) q^{61} +(-77.0000 + 400.104i) q^{63} +(49.0000 + 84.8705i) q^{65} +(207.500 - 359.401i) q^{67} -1113.00 q^{69} +432.000 q^{71} +(556.500 - 963.886i) q^{73} +(-266.000 - 460.726i) q^{75} +(87.5000 - 30.3109i) q^{77} +(-51.5000 - 89.2006i) q^{79} +(419.500 - 726.595i) q^{81} -1092.00 q^{83} -147.000 q^{85} +(203.000 - 351.606i) q^{87} +(164.500 + 284.922i) q^{89} +(196.000 + 169.741i) q^{91} +(-514.500 - 891.140i) q^{93} +(171.500 - 297.047i) q^{95} -882.000 q^{97} +110.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 7 q^{3} - 7 q^{5} - 28 q^{7} - 22 q^{9} - 5 q^{11} - 28 q^{13} - 98 q^{15} + 21 q^{17} + 49 q^{19} - 245 q^{21} - 159 q^{23} + 76 q^{25} + 70 q^{27} + 116 q^{29} + 147 q^{31} + 35 q^{33} - 49 q^{35}+ \cdots + 220 q^{99}+O(q^{100}) $ 2 * q + 7 * q^3 - 7 * q^5 - 28 * q^7 - 22 * q^9 - 5 * q^11 - 28 * q^13 - 98 * q^15 + 21 * q^17 + 49 * q^19 - 245 * q^21 - 159 * q^23 + 76 * q^25 + 70 * q^27 + 116 * q^29 + 147 * q^31 + 35 * q^33 - 49 * q^35 - 219 * q^37 - 98 * q^39 + 700 * q^41 + 248 * q^43 - 154 * q^45 + 525 * q^47 + 98 * q^49 - 147 * q^51 - 303 * q^53 + 70 * q^55 + 686 * q^57 - 105 * q^59 + 413 * q^61 - 154 * q^63 + 98 * q^65 + 415 * q^67 - 2226 * q^69 + 864 * q^71 + 1113 * q^73 - 532 * q^75 + 175 * q^77 - 103 * q^79 + 839 * q^81 - 2184 * q^83 - 294 * q^85 + 406 * q^87 + 329 * q^89 + 392 * q^91 - 1029 * q^93 + 343 * q^95 - 1764 * q^97 + 220 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	3.50000	−	6.06218i	0.673575	−	1.16667i	−0.303308	−	0.952893i	$-0.598091\pi$
$3$	3.50000	−	6.06218i	0.673575	−	1.16667i	0.976883	−	0.213774i	$-0.0685756\pi$
$4$		0			0
$5$	−3.50000	−	6.06218i	−0.313050	−	0.542218i	0.665971	−	0.745977i	$-0.268017\pi$
$5$	−3.50000	−	6.06218i	−0.313050	−	0.542218i	−0.979021	+	0.203760i	$0.934684\pi$
$6$		0			0
$7$	−14.0000	−	12.1244i	−0.755929	−	0.654654i
$7$	−14.0000	−	12.1244i	−0.755929	−	0.654654i
$8$		0			0
$9$	−11.0000	−	19.0526i	−0.407407	−	0.705650i
$10$		0			0
$11$	−2.50000	+	4.33013i	−0.0685253	+	0.118689i	−0.898252	−	0.439480i	$-0.855163\pi$
$11$	−2.50000	+	4.33013i	−0.0685253	+	0.118689i	0.829727	+	0.558169i	$0.188496\pi$
$12$		0			0
$13$	−14.0000			−0.298685			−0.149342	−	0.988786i	$-0.547716\pi$
$13$	−14.0000			−0.298685			−0.149342	+	0.988786i	$0.547716\pi$
$14$		0			0
$15$	−49.0000			−0.843450
$16$		0			0
$17$	10.5000	−	18.1865i	0.149801	−	0.259464i	−0.781353	−	0.624090i	$-0.785470\pi$
$17$	10.5000	−	18.1865i	0.149801	−	0.259464i	0.931154	+	0.364626i	$0.118803\pi$
$18$		0			0
$19$	24.5000	+	42.4352i	0.295826	+	0.512385i	0.975177	−	0.221429i	$-0.0710720\pi$
$19$	24.5000	+	42.4352i	0.295826	+	0.512385i	−0.679351	+	0.733813i	$0.737739\pi$
$20$		0			0
$21$	−122.500	+	42.4352i	−1.27294	+	0.440959i
$22$		0			0
$23$	−79.5000	−	137.698i	−0.720735	−	1.24835i	−0.960706	−	0.277569i	$-0.910471\pi$
$23$	−79.5000	−	137.698i	−0.720735	−	1.24835i	0.239971	−	0.970780i	$-0.422862\pi$
$24$		0			0
$25$	38.0000	−	65.8179i	0.304000	−	0.526543i
$26$		0			0
$27$	35.0000			0.249472
$28$		0			0
$29$	58.0000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	58.0000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$	73.5000	−	127.306i	0.425838	−	0.737574i	−0.570660	−	0.821186i	$-0.693313\pi$
$31$	73.5000	−	127.306i	0.425838	−	0.737574i	0.996498	+	0.0836128i	$0.0266459\pi$
$32$		0			0
$33$	17.5000	+	30.3109i	0.0923139	+	0.159892i
$34$		0			0
$35$	−24.5000	+	127.306i	−0.118322	+	0.614817i
$36$		0			0
$37$	−109.500	−	189.660i	−0.486532	−	0.842698i	0.513348	−	0.858181i	$-0.328405\pi$
$37$	−109.500	−	189.660i	−0.486532	−	0.842698i	−0.999880	+	0.0154821i	$0.995072\pi$
$38$		0			0
$39$	−49.0000	+	84.8705i	−0.201187	+	0.348466i
$40$		0			0
$41$	350.000			1.33319			0.666595	−	0.745420i	$-0.267751\pi$
$41$	350.000			1.33319			0.666595	+	0.745420i	$0.267751\pi$
$42$		0			0
$43$	124.000			0.439763			0.219882	−	0.975527i	$-0.429433\pi$
$43$	124.000			0.439763			0.219882	+	0.975527i	$0.429433\pi$
$44$		0			0
$45$	−77.0000	+	133.368i	−0.255077	+	0.441807i
$46$		0			0
$47$	262.500	+	454.663i	0.814671	+	1.41105i	0.909564	+	0.415565i	$0.136416\pi$
$47$	262.500	+	454.663i	0.814671	+	1.41105i	−0.0948921	+	0.995488i	$0.530251\pi$
$48$		0			0
$49$	49.0000	+	339.482i	0.142857	+	0.989743i
$50$		0			0
$51$	−73.5000	−	127.306i	−0.201805	−	0.349537i
$52$		0			0
$53$	−151.500	+	262.406i	−0.392644	+	0.680079i	−0.992797	−	0.119806i	$-0.961773\pi$
$53$	−151.500	+	262.406i	−0.392644	+	0.680079i	0.600153	+	0.799885i	$0.295106\pi$
$54$		0			0
$55$	35.0000			0.0858073
$56$		0			0
$57$	343.000			0.797043
$58$		0			0
$59$	−52.5000	+	90.9327i	−0.115846	+	0.200651i	−0.918118	−	0.396308i	$-0.870291\pi$
$59$	−52.5000	+	90.9327i	−0.115846	+	0.200651i	0.802272	+	0.596959i	$0.203625\pi$
$60$		0			0
$61$	206.500	+	357.668i	0.433436	+	0.750734i	0.997167	−	0.0752252i	$-0.0239676\pi$
$61$	206.500	+	357.668i	0.433436	+	0.750734i	−0.563730	+	0.825959i	$0.690634\pi$
$62$		0			0
$63$	−77.0000	+	400.104i	−0.153986	+	0.800132i
$64$		0			0
$65$	49.0000	+	84.8705i	0.0935031	+	0.161952i
$66$		0			0
$67$	207.500	−	359.401i	0.378361	−	0.655340i	−0.612463	−	0.790499i	$-0.709821\pi$
$67$	207.500	−	359.401i	0.378361	−	0.655340i	0.990824	+	0.135159i	$0.0431546\pi$
$68$		0			0
$69$	−1113.00			−1.94188
$70$		0			0
$71$	432.000			0.722098			0.361049	−	0.932547i	$-0.382419\pi$
$71$	432.000			0.722098			0.361049	+	0.932547i	$0.382419\pi$
$72$		0			0
$73$	556.500	−	963.886i	0.892238	−	1.54540i	0.0550526	−	0.998483i	$-0.482467\pi$
$73$	556.500	−	963.886i	0.892238	−	1.54540i	0.837186	−	0.546919i	$-0.184199\pi$
$74$		0			0
$75$	−266.000	−	460.726i	−0.409534	−	0.709333i
$76$		0			0
$77$	87.5000	−	30.3109i	0.129501	−	0.0448603i
$78$		0			0
$79$	−51.5000	−	89.2006i	−0.0733443	−	0.127036i	0.827021	−	0.562171i	$-0.190034\pi$
$79$	−51.5000	−	89.2006i	−0.0733443	−	0.127036i	−0.900365	+	0.435135i	$0.856701\pi$
$80$		0			0
$81$	419.500	−	726.595i	0.575446	−	0.996701i
$82$		0			0
$83$	−1092.00			−1.44413			−0.722064	−	0.691827i	$-0.756806\pi$
$83$	−1092.00			−1.44413			−0.722064	+	0.691827i	$0.756806\pi$
$84$		0			0
$85$	−147.000			−0.187581
$86$		0			0
$87$	203.000	−	351.606i	0.250160	−	0.433289i
$88$		0			0
$89$	164.500	+	284.922i	0.195921	+	0.339345i	0.947202	−	0.320637i	$-0.103897\pi$
$89$	164.500	+	284.922i	0.195921	+	0.339345i	−0.751281	+	0.659982i	$0.770564\pi$
$90$		0			0
$91$	196.000	+	169.741i	0.225784	+	0.195535i
$92$		0			0
$93$	−514.500	−	891.140i	−0.573668	−	0.993623i
$94$		0			0
$95$	171.500	−	297.047i	0.185216	−	0.320804i
$96$		0			0
$97$	−882.000			−0.923232			−0.461616	−	0.887080i	$-0.652730\pi$
$97$	−882.000			−0.923232			−0.461616	+	0.887080i	$0.652730\pi$
$98$		0			0
$99$	110.000			0.111671
$100$		0			0
$101$	−689.500	+	1194.25i	−0.679285	+	1.17656i	0.295911	+	0.955215i	$0.404377\pi$
$101$	−689.500	+	1194.25i	−0.679285	+	1.17656i	−0.975196	+	0.221341i	$0.928957\pi$
$102$		0			0
$103$	−339.500	−	588.031i	−0.324776	−	0.562529i	0.656691	−	0.754160i	$-0.271956\pi$
$103$	−339.500	−	588.031i	−0.324776	−	0.562529i	−0.981467	+	0.191631i	$0.938622\pi$
$104$		0			0
$105$	686.000	+	594.093i	0.637588	+	0.552167i
$106$		0			0
$107$	228.500	+	395.774i	0.206448	+	0.357578i	0.950593	−	0.310440i	$-0.100476\pi$
$107$	228.500	+	395.774i	0.206448	+	0.357578i	−0.744145	+	0.668018i	$0.767143\pi$
$108$		0			0
$109$	562.500	−	974.279i	0.494291	−	0.856137i	−0.505687	−	0.862717i	$-0.668761\pi$
$109$	562.500	−	974.279i	0.494291	−	0.856137i	0.999978	+	0.00657959i	$0.00209436\pi$
$110$		0			0
$111$	−1533.00			−1.31086
$112$		0			0
$113$	−1538.00			−1.28038			−0.640190	−	0.768217i	$-0.721144\pi$
$113$	−1538.00			−1.28038			−0.640190	+	0.768217i	$0.721144\pi$
$114$		0			0
$115$	−556.500	+	963.886i	−0.451251	+	0.781590i
$116$		0			0
$117$	154.000	+	266.736i	0.121686	+	0.210767i
$118$		0			0
$119$	−367.500	+	127.306i	−0.283098	+	0.0980680i
$120$		0			0
$121$	653.000	+	1131.03i	0.490609	+	0.849759i
$122$		0			0
$123$	1225.00	−	2121.76i	0.898004	−	1.55539i
$124$		0			0
$125$	−1407.00			−1.00677
$126$		0			0
$127$	−72.0000			−0.0503068			−0.0251534	−	0.999684i	$-0.508007\pi$
$127$	−72.0000			−0.0503068			−0.0251534	+	0.999684i	$0.508007\pi$
$128$		0			0
$129$	434.000	−	751.710i	0.296214	−	0.513057i
$130$		0			0
$131$	1074.50	+	1861.09i	0.716637	+	1.24125i	0.962325	+	0.271903i	$0.0876531\pi$
$131$	1074.50	+	1861.09i	0.716637	+	1.24125i	−0.245687	+	0.969349i	$0.579014\pi$
$132$		0			0
$133$	171.500	−	891.140i	0.111812	−	0.580990i
$134$		0			0
$135$	−122.500	−	212.176i	−0.0780972	−	0.135268i
$136$		0			0
$137$	562.500	−	974.279i	0.350786	−	0.607578i	−0.635602	−	0.772017i	$-0.719248\pi$
$137$	562.500	−	974.279i	0.350786	−	0.607578i	0.986387	+	0.164439i	$0.0525813\pi$
$138$		0			0
$139$	−252.000			−0.153772			−0.0768862	−	0.997040i	$-0.524498\pi$
$139$	−252.000			−0.153772			−0.0768862	+	0.997040i	$0.524498\pi$
$140$		0			0
$141$	3675.00			2.19497
$142$		0			0
$143$	35.0000	−	60.6218i	0.0204675	−	0.0354507i
$144$		0			0
$145$	−203.000	−	351.606i	−0.116264	−	0.201375i
$146$		0			0
$147$	2229.50	+	891.140i	1.25093	+	0.500000i
$148$		0			0
$149$	100.500	+	174.071i	0.0552569	+	0.0957078i	0.892331	−	0.451382i	$-0.149069\pi$
$149$	100.500	+	174.071i	0.0552569	+	0.0957078i	−0.837074	+	0.547090i	$0.815736\pi$
$150$		0			0
$151$	809.500	−	1402.10i	0.436266	−	0.755635i	−0.561132	−	0.827726i	$-0.689634\pi$
$151$	809.500	−	1402.10i	0.436266	−	0.755635i	0.997398	+	0.0720914i	$0.0229673\pi$
$152$		0			0
$153$	−462.000			−0.244121
$154$		0			0
$155$	−1029.00			−0.533234
$156$		0			0
$157$	−339.500	+	588.031i	−0.172580	+	0.298917i	−0.939321	−	0.343039i	$-0.888544\pi$
$157$	−339.500	+	588.031i	−0.172580	+	0.298917i	0.766741	+	0.641956i	$0.221877\pi$
$158$		0			0
$159$	1060.50	+	1836.84i	0.528950	+	0.916169i
$160$		0			0
$161$	−556.500	+	2891.66i	−0.272412	+	1.41549i
$162$		0			0
$163$	−233.500	−	404.434i	−0.112203	−	0.194342i	0.804455	−	0.594014i	$-0.202457\pi$
$163$	−233.500	−	404.434i	−0.112203	−	0.194342i	−0.916658	+	0.399672i	$0.869124\pi$
$164$		0			0
$165$	122.500	−	212.176i	0.0577976	−	0.100108i
$166$		0			0
$167$	−1204.00			−0.557894			−0.278947	−	0.960306i	$-0.589985\pi$
$167$	−1204.00			−0.557894			−0.278947	+	0.960306i	$0.589985\pi$
$168$		0			0
$169$	−2001.00			−0.910787
$170$		0			0
$171$	539.000	−	933.575i	0.241043	−	0.417499i
$172$		0			0
$173$	1410.50	+	2443.06i	0.619875	+	1.07365i	0.989508	+	0.144477i	$0.0461499\pi$
$173$	1410.50	+	2443.06i	0.619875	+	1.07365i	−0.369633	+	0.929178i	$0.620517\pi$
$174$		0			0
$175$	−1330.00	+	460.726i	−0.574506	+	0.199015i
$176$		0			0
$177$	367.500	+	636.529i	0.156062	+	0.270307i
$178$		0			0
$179$	−1626.50	+	2817.18i	−0.679164	+	1.17635i	0.296069	+	0.955166i	$0.404324\pi$
$179$	−1626.50	+	2817.18i	−0.679164	+	1.17635i	−0.975233	+	0.221180i	$0.929009\pi$
$180$		0			0
$181$	1582.00			0.649664			0.324832	−	0.945772i	$-0.394692\pi$
$181$	1582.00			0.649664			0.324832	+	0.945772i	$0.394692\pi$
$182$		0			0
$183$	2891.00			1.16781
$184$		0			0
$185$	−766.500	+	1327.62i	−0.304617	+	0.527613i
$186$		0			0
$187$	52.5000	+	90.9327i	0.0205304	+	0.0355597i
$188$		0			0
$189$	−490.000	−	424.352i	−0.188583	−	0.163318i
$190$		0			0
$191$	1278.50	+	2214.43i	0.484340	+	0.838902i	0.999838	−	0.0179887i	$-0.00572630\pi$
$191$	1278.50	+	2214.43i	0.484340	+	0.838902i	−0.515498	+	0.856891i	$0.672393\pi$
$192$		0			0
$193$	198.500	−	343.812i	0.0740329	−	0.128229i	−0.826632	−	0.562742i	$-0.809746\pi$
$193$	198.500	−	343.812i	0.0740329	−	0.128229i	0.900665	+	0.434514i	$0.143080\pi$
$194$		0			0
$195$	686.000			0.251926
$196$		0			0
$197$	2914.00			1.05388			0.526939	−	0.849903i	$-0.323340\pi$
$197$	2914.00			1.05388			0.526939	+	0.849903i	$0.323340\pi$
$198$		0			0
$199$	1669.50	−	2891.66i	0.594712	−	1.03007i	−0.398875	−	0.917005i	$-0.630599\pi$
$199$	1669.50	−	2891.66i	0.594712	−	1.03007i	0.993587	−	0.113066i	$-0.0360673\pi$
$200$		0			0
$201$	−1452.50	−	2515.80i	−0.509709	−	0.882841i
$202$		0			0
$203$	−812.000	−	703.213i	−0.280745	−	0.243132i
$204$		0			0
$205$	−1225.00	−	2121.76i	−0.417355	−	0.722880i
$206$		0			0
$207$	−1749.00	+	3029.36i	−0.587265	+	1.01717i
$208$		0			0
$209$	−245.000			−0.0810861
$210$		0			0
$211$	−1780.00			−0.580759			−0.290380	−	0.956911i	$-0.593782\pi$
$211$	−1780.00			−0.580759			−0.290380	+	0.956911i	$0.593782\pi$
$212$		0			0
$213$	1512.00	−	2618.86i	0.486387	−	0.842448i
$214$		0			0
$215$	−434.000	−	751.710i	−0.137668	−	0.238447i
$216$		0			0
$217$	−2572.50	+	891.140i	−0.804759	+	0.278777i
$218$		0			0
$219$	−3895.50	−	6747.20i	−1.20198	−	2.08189i
$220$		0			0
$221$	−147.000	+	254.611i	−0.0447434	+	0.0774978i
$222$		0			0
$223$	1400.00			0.420408			0.210204	−	0.977658i	$-0.432587\pi$
$223$	1400.00			0.420408			0.210204	+	0.977658i	$0.432587\pi$
$224$		0			0
$225$	−1672.00			−0.495407
$226$		0			0
$227$	−1102.50	+	1909.59i	−0.322359	+	0.558342i	−0.980974	−	0.194138i	$-0.937809\pi$
$227$	−1102.50	+	1909.59i	−0.322359	+	0.558342i	0.658615	+	0.752480i	$0.271142\pi$
$228$		0			0
$229$	−143.500	−	248.549i	−0.0414094	−	0.0717231i	0.844578	−	0.535433i	$-0.179851\pi$
$229$	−143.500	−	248.549i	−0.0414094	−	0.0717231i	−0.885987	+	0.463710i	$0.846518\pi$
$230$		0			0
$231$	122.500	−	636.529i	0.0348914	−	0.181301i
$232$		0			0
$233$	−2293.50	−	3972.46i	−0.644859	−	1.11693i	−0.984334	−	0.176314i	$-0.943583\pi$
$233$	−2293.50	−	3972.46i	−0.644859	−	1.11693i	0.339475	−	0.940615i	$-0.389751\pi$
$234$		0			0
$235$	1837.50	−	3182.64i	0.510065	−	0.883459i
$236$		0			0
$237$	−721.000			−0.197612
$238$		0			0
$239$	−1668.00			−0.451439			−0.225720	−	0.974192i	$-0.572473\pi$
$239$	−1668.00			−0.451439			−0.225720	+	0.974192i	$0.572473\pi$
$240$		0			0
$241$	1704.50	−	2952.28i	0.455587	−	0.789100i	−0.543135	−	0.839646i	$-0.682763\pi$
$241$	1704.50	−	2952.28i	0.455587	−	0.789100i	0.998722	+	0.0505456i	$0.0160960\pi$
$242$		0			0
$243$	−2464.00	−	4267.77i	−0.650476	−	1.12666i
$244$		0			0
$245$	1886.50	−	1485.23i	0.491935	−	0.387298i
$246$		0			0
$247$	−343.000	−	594.093i	−0.0883586	−	0.153042i
$248$		0			0
$249$	−3822.00	+	6619.90i	−0.972729	+	1.68482i
$250$		0			0
$251$	4760.00			1.19701			0.598503	−	0.801121i	$-0.295762\pi$
$251$	4760.00			1.19701			0.598503	+	0.801121i	$0.295762\pi$
$252$		0			0
$253$	795.000			0.197554
$254$		0			0
$255$	−514.500	+	891.140i	−0.126350	+	0.218845i
$256$		0			0
$257$	402.500	+	697.150i	0.0976936	+	0.169210i	0.910730	−	0.413003i	$-0.135520\pi$
$257$	402.500	+	697.150i	0.0976936	+	0.169210i	−0.813036	+	0.582213i	$0.802187\pi$
$258$		0			0
$259$	−766.500	+	3982.85i	−0.183892	+	0.955530i
$260$		0			0
$261$	−638.000	−	1105.05i	−0.151307	−	0.262072i
$262$		0			0
$263$	−128.500	+	222.569i	−0.0301279	+	0.0521831i	−0.880696	−	0.473681i	$-0.842925\pi$
$263$	−128.500	+	222.569i	−0.0301279	+	0.0521831i	0.850568	+	0.525865i	$0.176258\pi$
$264$		0			0
$265$	2121.00			0.491668
$266$		0			0
$267$	2303.00			0.527870
$268$		0			0
$269$	−1795.50	+	3109.90i	−0.406965	+	0.704884i	−0.994548	−	0.104280i	$-0.966746\pi$
$269$	−1795.50	+	3109.90i	−0.406965	+	0.704884i	0.587583	+	0.809164i	$0.300080\pi$
$270$		0			0
$271$	696.500	+	1206.37i	0.156123	+	0.270413i	0.933467	−	0.358662i	$-0.116767\pi$
$271$	696.500	+	1206.37i	0.156123	+	0.270413i	−0.777344	+	0.629075i	$0.783434\pi$
$272$		0			0
$273$	1715.00	−	594.093i	0.380207	−	0.131708i
$274$		0			0
$275$	190.000	+	329.090i	0.0416634	+	0.0721631i
$276$		0			0
$277$	−207.500	+	359.401i	−0.0450089	+	0.0779577i	−0.887652	−	0.460514i	$-0.847665\pi$
$277$	−207.500	+	359.401i	−0.0450089	+	0.0779577i	0.842643	+	0.538472i	$0.180998\pi$
$278$		0			0
$279$	−3234.00			−0.693959
$280$		0			0
$281$	−4954.00			−1.05171			−0.525856	−	0.850574i	$-0.676255\pi$
$281$	−4954.00			−1.05171			−0.525856	+	0.850574i	$0.676255\pi$
$282$		0			0
$283$	−2138.50	+	3703.99i	−0.449190	+	0.778019i	−0.998333	−	0.0577087i	$-0.981621\pi$
$283$	−2138.50	+	3703.99i	−0.449190	+	0.778019i	0.549144	+	0.835728i	$0.314954\pi$
$284$		0			0
$285$	−1200.50	−	2079.33i	−0.249514	−	0.432171i
$286$		0			0
$287$	−4900.00	−	4243.52i	−1.00780	−	0.872778i
$288$		0			0
$289$	2236.00	+	3872.87i	0.455119	+	0.788289i
$290$		0			0
$291$	−3087.00	+	5346.84i	−0.621866	+	1.07710i
$292$		0			0
$293$	7742.00			1.54366			0.771830	−	0.635829i	$-0.219342\pi$
$293$	7742.00			1.54366			0.771830	+	0.635829i	$0.219342\pi$
$294$		0			0
$295$	735.000			0.145062
$296$		0			0
$297$	−87.5000	+	151.554i	−0.0170952	+	0.0296097i
$298$		0			0
$299$	1113.00	+	1927.77i	0.215272	+	0.372863i
$300$		0			0
$301$	−1736.00	−	1503.42i	−0.332430	−	0.287893i
$302$		0			0
$303$	4826.50	+	8359.74i	0.915100	+	1.58500i
$304$		0			0
$305$	1445.50	−	2503.68i	0.271374	−	0.470034i
$306$		0			0
$307$	7364.00			1.36901			0.684504	−	0.729009i	$-0.260019\pi$
$307$	7364.00			1.36901			0.684504	+	0.729009i	$0.260019\pi$
$308$		0			0
$309$	−4753.00			−0.875044
$310$		0			0
$311$	4987.50	−	8638.60i	0.909374	−	1.57508i	0.0944372	−	0.995531i	$-0.469895\pi$
$311$	4987.50	−	8638.60i	0.909374	−	1.57508i	0.814936	−	0.579550i	$-0.196772\pi$
$312$		0			0
$313$	2376.50	+	4116.22i	0.429162	+	0.743330i	0.996799	−	0.0799485i	$-0.0254756\pi$
$313$	2376.50	+	4116.22i	0.429162	+	0.743330i	−0.567637	+	0.823279i	$0.692142\pi$
$314$		0			0
$315$	2695.00	−	933.575i	0.482051	−	0.166987i
$316$		0			0
$317$	1738.50	+	3011.17i	0.308025	+	0.533515i	0.977930	−	0.208932i	$-0.0669987\pi$
$317$	1738.50	+	3011.17i	0.308025	+	0.533515i	−0.669905	+	0.742447i	$0.733665\pi$
$318$		0			0
$319$	−145.000	+	251.147i	−0.0254497	+	0.0440801i
$320$		0			0
$321$	3199.00			0.556233
$322$		0			0
$323$	1029.00			0.177260
$324$		0			0
$325$	−532.000	+	921.451i	−0.0908002	+	0.157270i
$326$		0			0
$327$	−3937.50	−	6819.95i	−0.665885	−	1.15335i
$328$		0			0
$329$	1837.50	−	9547.93i	0.307917	−	1.59998i
$330$		0			0
$331$	1670.50	+	2893.39i	0.277399	+	0.480469i	0.970738	−	0.240143i	$-0.0771944\pi$
$331$	1670.50	+	2893.39i	0.277399	+	0.480469i	−0.693339	+	0.720612i	$0.743861\pi$
$332$		0			0
$333$	−2409.00	+	4172.51i	−0.396434	+	0.686643i
$334$		0			0
$335$	−2905.00			−0.473782
$336$		0			0
$337$	7366.00			1.19066			0.595329	−	0.803482i	$-0.297022\pi$
$337$	7366.00			1.19066			0.595329	+	0.803482i	$0.297022\pi$
$338$		0			0
$339$	−5383.00	+	9323.63i	−0.862432	+	1.49378i
$340$		0			0
$341$	367.500	+	636.529i	0.0583614	+	0.101085i
$342$		0			0
$343$	3430.00	−	5346.84i	0.539949	−	0.841698i
$344$		0			0
$345$	3895.50	+	6747.20i	0.607903	+	1.05292i
$346$		0			0
$347$	3707.50	−	6421.58i	0.573571	−	0.993454i	−0.422625	−	0.906305i	$-0.638891\pi$
$347$	3707.50	−	6421.58i	0.573571	−	0.993454i	0.996195	−	0.0871487i	$-0.0277755\pi$
$348$		0			0
$349$	−3878.00			−0.594798			−0.297399	−	0.954753i	$-0.596119\pi$
$349$	−3878.00			−0.594798			−0.297399	+	0.954753i	$0.596119\pi$
$350$		0			0
$351$	−490.000			−0.0745136
$352$		0			0
$353$	−633.500	+	1097.25i	−0.0955179	+	0.165442i	−0.909825	−	0.414993i	$-0.863784\pi$
$353$	−633.500	+	1097.25i	−0.0955179	+	0.165442i	0.814307	+	0.580435i	$0.197117\pi$
$354$		0			0
$355$	−1512.00	−	2618.86i	−0.226052	−	0.391534i
$356$		0			0
$357$	−514.500	+	2673.42i	−0.0762751	+	0.396337i
$358$		0			0
$359$	2342.50	+	4057.33i	0.344380	+	0.596484i	0.985241	−	0.171173i	$-0.0547558\pi$
$359$	2342.50	+	4057.33i	0.344380	+	0.596484i	−0.640861	+	0.767657i	$0.721422\pi$
$360$		0			0
$361$	2229.00	−	3860.74i	0.324974	−	0.562872i
$362$		0			0
$363$	9142.00			1.32185
$364$		0			0
$365$	−7791.00			−1.11726
$366$		0			0
$367$	−2320.50	+	4019.22i	−0.330052	+	0.571667i	−0.982522	−	0.186148i	$-0.940400\pi$
$367$	−2320.50	+	4019.22i	−0.330052	+	0.571667i	0.652470	+	0.757815i	$0.273733\pi$
$368$		0			0
$369$	−3850.00	−	6668.40i	−0.543152	−	0.940766i
$370$		0			0
$371$	5302.50	−	1836.84i	0.742027	−	0.257046i
$372$		0			0
$373$	4398.50	+	7618.43i	0.610578	+	1.05755i	0.991143	+	0.132798i	$0.0423963\pi$
$373$	4398.50	+	7618.43i	0.610578	+	1.05755i	−0.380565	+	0.924754i	$0.624270\pi$
$374$		0			0
$375$	−4924.50	+	8529.48i	−0.678134	+	1.17456i
$376$		0			0
$377$	−812.000			−0.110929
$378$		0			0
$379$	−13680.0			−1.85407			−0.927037	−	0.374969i	$-0.877653\pi$
$379$	−13680.0			−1.85407			−0.927037	+	0.374969i	$0.877653\pi$
$380$		0			0
$381$	−252.000	+	436.477i	−0.0338854	+	0.0586913i
$382$		0			0
$383$	4882.50	+	8456.74i	0.651395	+	1.12825i	0.982785	+	0.184755i	$0.0591490\pi$
$383$	4882.50	+	8456.74i	0.651395	+	1.12825i	−0.331390	+	0.943494i	$0.607518\pi$
$384$		0			0
$385$	−490.000	−	424.352i	−0.0648642	−	0.0561740i
$386$		0			0
$387$	−1364.00	−	2362.52i	−0.179163	−	0.310319i
$388$		0			0
$389$	−865.500	+	1499.09i	−0.112809	+	0.195390i	−0.916902	−	0.399113i	$-0.869318\pi$
$389$	−865.500	+	1499.09i	−0.112809	+	0.195390i	0.804093	+	0.594504i	$0.202651\pi$
$390$		0			0
$391$	−3339.00			−0.431868
$392$		0			0
$393$	15043.0			1.93084
$394$		0			0
$395$	−360.500	+	624.404i	−0.0459208	+	0.0795372i
$396$		0			0
$397$	−5491.50	−	9511.56i	−0.694233	−	1.20245i	−0.970439	−	0.241348i	$-0.922410\pi$
$397$	−5491.50	−	9511.56i	−0.694233	−	1.20245i	0.276206	−	0.961099i	$-0.410923\pi$
$398$		0			0
$399$	−4802.00	−	4158.65i	−0.602508	−	0.521787i
$400$		0			0
$401$	−3301.50	−	5718.37i	−0.411145	−	0.712124i	0.583870	−	0.811847i	$-0.301538\pi$
$401$	−3301.50	−	5718.37i	−0.411145	−	0.712124i	−0.995015	+	0.0997232i	$0.968204\pi$
$402$		0			0
$403$	−1029.00	+	1782.28i	−0.127191	+	0.220302i
$404$		0			0
$405$	−5873.00			−0.720572
$406$		0			0
$407$	1095.00			0.133359
$408$		0			0
$409$	−5477.50	+	9487.31i	−0.662213	+	1.14699i	0.317820	+	0.948151i	$0.397049\pi$
$409$	−5477.50	+	9487.31i	−0.662213	+	1.14699i	−0.980033	+	0.198835i	$0.936284\pi$
$410$		0			0
$411$	−3937.50	−	6819.95i	−0.472561	−	0.818500i
$412$		0			0
$413$	1837.50	−	636.529i	0.218928	−	0.0758391i
$414$		0			0
$415$	3822.00	+	6619.90i	0.452083	+	0.783031i
$416$		0			0
$417$	−882.000	+	1527.67i	−0.103577	+	0.179401i
$418$		0			0
$419$	−6636.00			−0.773723			−0.386861	−	0.922138i	$-0.626441\pi$
$419$	−6636.00			−0.773723			−0.386861	+	0.922138i	$0.626441\pi$
$420$		0			0
$421$	−16630.0			−1.92517			−0.962585	−	0.270980i	$-0.912652\pi$
$421$	−16630.0			−1.92517			−0.962585	+	0.270980i	$0.912652\pi$
$422$		0			0
$423$	5775.00	−	10002.6i	0.663806	−	1.14975i
$424$		0			0
$425$	−798.000	−	1382.18i	−0.0910793	−	0.157754i
$426$		0			0
$427$	1445.50	−	7511.04i	0.163824	−	0.851252i
$428$		0			0
$429$	−245.000	−	424.352i	−0.0275728	−	0.0477574i
$430$		0			0
$431$	2461.50	−	4263.44i	0.275096	−	0.476480i	−0.695064	−	0.718948i	$-0.744624\pi$
$431$	2461.50	−	4263.44i	0.275096	−	0.476480i	0.970159	+	0.242468i	$0.0779571\pi$
$432$		0			0
$433$	8974.00			0.995988			0.497994	−	0.867180i	$-0.334070\pi$
$433$	8974.00			0.995988			0.497994	+	0.867180i	$0.334070\pi$
$434$		0			0
$435$	−2842.00			−0.313249
$436$		0			0
$437$	3895.50	−	6747.20i	0.426423	−	0.738587i
$438$		0			0
$439$	−2089.50	−	3619.12i	−0.227167	−	0.393465i	0.729800	−	0.683660i	$-0.239613\pi$
$439$	−2089.50	−	3619.12i	−0.227167	−	0.393465i	−0.956967	+	0.290195i	$0.906280\pi$
$440$		0			0
$441$	5929.00	−	4667.88i	0.640212	−	0.504036i
$442$		0			0
$443$	−6463.50	−	11195.1i	−0.693206	−	1.20067i	−0.970782	−	0.239964i	$-0.922864\pi$
$443$	−6463.50	−	11195.1i	−0.693206	−	1.20067i	0.277576	−	0.960704i	$-0.410469\pi$
$444$		0			0
$445$	1151.50	−	1994.46i	0.122666	−	0.212464i
$446$		0			0
$447$	1407.00			0.148879
$448$		0			0
$449$	−2826.00			−0.297032			−0.148516	−	0.988910i	$-0.547450\pi$
$449$	−2826.00			−0.297032			−0.148516	+	0.988910i	$0.547450\pi$
$450$		0			0
$451$	−875.000	+	1515.54i	−0.0913573	+	0.158235i
$452$		0			0
$453$	−5666.50	−	9814.67i	−0.587716	−	1.01795i
$454$		0			0
$455$	343.000	−	1782.28i	0.0353409	−	0.183636i
$456$		0			0
$457$	−4239.50	−	7343.03i	−0.433951	−	0.751625i	0.563259	−	0.826281i	$-0.309547\pi$
$457$	−4239.50	−	7343.03i	−0.433951	−	0.751625i	−0.997209	+	0.0746560i	$0.976214\pi$
$458$		0			0
$459$	367.500	−	636.529i	0.0373713	−	0.0647290i
$460$		0			0
$461$	9338.00			0.943414			0.471707	−	0.881755i	$-0.343638\pi$
$461$	9338.00			0.943414			0.471707	+	0.881755i	$0.343638\pi$
$462$		0			0
$463$	4016.00			0.403109			0.201554	−	0.979477i	$-0.435401\pi$
$463$	4016.00			0.403109			0.201554	+	0.979477i	$0.435401\pi$
$464$		0			0
$465$	−3601.50	+	6237.98i	−0.359173	+	0.622106i
$466$		0			0
$467$	−2929.50	−	5074.04i	−0.290281	−	0.502781i	0.683595	−	0.729861i	$-0.260415\pi$
$467$	−2929.50	−	5074.04i	−0.290281	−	0.502781i	−0.973876	+	0.227080i	$0.927082\pi$
$468$		0			0
$469$	−7262.50	+	2515.80i	−0.715034	+	0.247695i
$470$		0			0
$471$	2376.50	+	4116.22i	0.232491	+	0.402687i
$472$		0			0
$473$	−310.000	+	536.936i	−0.0301349	+	0.0521952i
$474$		0			0
$475$	3724.00			0.359724
$476$		0			0
$477$	6666.00			0.639864
$478$		0			0
$479$	3251.50	−	5631.76i	0.310156	−	0.537206i	−0.668240	−	0.743946i	$-0.732952\pi$
$479$	3251.50	−	5631.76i	0.310156	−	0.537206i	0.978396	+	0.206740i	$0.0662853\pi$
$480$		0			0
$481$	1533.00	+	2655.23i	0.145320	+	0.251701i
$482$		0			0
$483$	15582.0	+	13494.4i	1.46792	+	1.27126i
$484$		0			0
$485$	3087.00	+	5346.84i	0.289017	+	0.500593i
$486$		0			0
$487$	−8024.50	+	13898.8i	−0.746663	+	1.29326i	0.202751	+	0.979230i	$0.435012\pi$
$487$	−8024.50	+	13898.8i	−0.746663	+	1.29326i	−0.949414	+	0.314028i	$0.898322\pi$
$488$		0			0
$489$	−3269.00			−0.302309
$490$		0			0
$491$	−8864.00			−0.814718			−0.407359	−	0.913268i	$-0.633550\pi$
$491$	−8864.00			−0.814718			−0.407359	+	0.913268i	$0.633550\pi$
$492$		0			0
$493$	609.000	−	1054.82i	0.0556348	−	0.0963624i
$494$		0			0
$495$	−385.000	−	666.840i	−0.0349585	−	0.0605499i
$496$		0			0
$497$	−6048.00	−	5237.72i	−0.545855	−	0.472724i
$498$		0			0
$499$	−5105.50	−	8842.99i	−0.458023	−	0.793319i	0.540833	−	0.841130i	$-0.318109\pi$
$499$	−5105.50	−	8842.99i	−0.458023	−	0.793319i	−0.998856	+	0.0478104i	$0.984776\pi$
$500$		0			0
$501$	−4214.00	+	7298.86i	−0.375784	+	0.650876i
$502$		0			0
$503$	1680.00			0.148921			0.0744607	−	0.997224i	$-0.476276\pi$
$503$	1680.00			0.148921			0.0744607	+	0.997224i	$0.476276\pi$
$504$		0			0
$505$	9653.00			0.850600
$506$		0			0
$507$	−7003.50	+	12130.4i	−0.613484	+	1.06259i
$508$		0			0
$509$	4728.50	+	8190.00i	0.411762	+	0.713193i	0.995083	−	0.0990489i	$-0.0315800\pi$
$509$	4728.50	+	8190.00i	0.411762	+	0.713193i	−0.583320	+	0.812242i	$0.698247\pi$
$510$		0			0
$511$	−19477.5	+	6747.20i	−1.68617	+	0.584107i
$512$		0			0
$513$	857.500	+	1485.23i	0.0738003	+	0.127826i
$514$		0			0
$515$	−2376.50	+	4116.22i	−0.203342	+	0.352199i
$516$		0			0
$517$	−2625.00			−0.223302
$518$		0			0
$519$	19747.0			1.67013
$520$		0			0
$521$	9040.50	−	15658.6i	0.760214	−	1.31673i	−0.182526	−	0.983201i	$-0.558427\pi$
$521$	9040.50	−	15658.6i	0.760214	−	1.31673i	0.942740	−	0.333528i	$-0.108239\pi$
$522$		0			0
$523$	10188.5	+	17647.0i	0.851839	+	1.47543i	0.879546	+	0.475813i	$0.157846\pi$
$523$	10188.5	+	17647.0i	0.851839	+	1.47543i	−0.0277071	+	0.999616i	$0.508821\pi$
$524$		0			0
$525$	−1862.00	+	9675.24i	−0.154789	+	0.804308i
$526$		0			0
$527$	−1543.50	−	2673.42i	−0.127582	−	0.220979i
$528$		0			0
$529$	−6557.00	+	11357.1i	−0.538917	+	0.933431i
$530$		0			0
$531$	2310.00			0.188786
$532$		0			0
$533$	−4900.00			−0.398204
$534$		0			0
$535$	1599.50	−	2770.42i	0.129257	−	0.223879i
$536$		0			0
$537$	11385.5	+	19720.3i	0.914936	+	1.58472i
$538$		0			0
$539$	−1592.50	−	636.529i	−0.127261	−	0.0508668i
$540$		0			0
$541$	3096.50	+	5363.30i	0.246079	+	0.426222i	0.962435	−	0.271514i	$-0.0875243\pi$
$541$	3096.50	+	5363.30i	0.246079	+	0.426222i	−0.716355	+	0.697736i	$0.754191\pi$
$542$		0			0
$543$	5537.00	−	9590.37i	0.437597	−	0.757941i
$544$		0			0
$545$	−7875.00			−0.618950
$546$		0			0
$547$	18464.0			1.44326			0.721630	−	0.692279i	$-0.243393\pi$
$547$	18464.0			1.44326			0.721630	+	0.692279i	$0.243393\pi$
$548$		0			0
$549$	4543.00	−	7868.71i	0.353170	−	0.611709i
$550$		0			0
$551$	1421.00	+	2461.24i	0.109867	+	0.190295i
$552$		0			0
$553$	−360.500	+	1873.21i	−0.0277216	+	0.144045i
$554$		0			0
$555$	5365.50	+	9293.32i	0.410365	+	0.710774i
$556$		0			0
$557$	4706.50	−	8151.90i	0.358027	−	0.620120i	−0.629604	−	0.776916i	$-0.716783\pi$
$557$	4706.50	−	8151.90i	0.358027	−	0.620120i	0.987631	+	0.156796i	$0.0501164\pi$
$558$		0			0
$559$	−1736.00			−0.131351
$560$		0			0
$561$	735.000			0.0553150
$562$		0			0
$563$	1599.50	−	2770.42i	0.119735	−	0.207387i	−0.799928	−	0.600097i	$-0.795129\pi$
$563$	1599.50	−	2770.42i	0.119735	−	0.207387i	0.919663	+	0.392709i	$0.128462\pi$
$564$		0			0
$565$	5383.00	+	9323.63i	0.400822	+	0.694244i
$566$		0			0
$567$	−14682.5	+	5086.17i	−1.08749	+	0.376718i
$568$		0			0
$569$	−10791.5	−	18691.4i	−0.795085	−	1.37713i	−0.922785	−	0.385314i	$-0.874093\pi$
$569$	−10791.5	−	18691.4i	−0.795085	−	1.37713i	0.127701	−	0.991813i	$-0.459240\pi$
$570$		0			0
$571$	10133.5	−	17551.7i	0.742686	−	1.28637i	−0.208582	−	0.978005i	$-0.566885\pi$
$571$	10133.5	−	17551.7i	0.742686	−	1.28637i	0.951268	−	0.308365i	$-0.0997819\pi$
$572$		0			0
$573$	17899.0			1.30496
$574$		0			0
$575$	−12084.0			−0.876413
$576$		0			0
$577$	−6975.50	+	12081.9i	−0.503282	+	0.871710i	0.496711	+	0.867916i	$0.334541\pi$
$577$	−6975.50	+	12081.9i	−0.503282	+	0.871710i	−0.999993	+	0.00379418i	$0.998792\pi$
$578$		0			0
$579$	−1389.50	−	2406.68i	−0.0997334	−	0.172743i
$580$		0			0
$581$	15288.0	+	13239.8i	1.09166	+	0.945403i
$582$		0			0
$583$	−757.500	−	1312.03i	−0.0538121	−	0.0932053i
$584$		0			0
$585$	1078.00	−	1867.15i	0.0761877	−	0.131961i
$586$		0			0
$587$	20972.0			1.47463			0.737314	−	0.675550i	$-0.236094\pi$
$587$	20972.0			1.47463			0.737314	+	0.675550i	$0.236094\pi$
$588$		0			0
$589$	7203.00			0.503895
$590$		0			0
$591$	10199.0	−	17665.2i	0.709866	−	1.22952i
$592$		0			0
$593$	94.5000	+	163.679i	0.00654410	+	0.0113347i	0.869279	−	0.494322i	$-0.164584\pi$
$593$	94.5000	+	163.679i	0.00654410	+	0.0113347i	−0.862735	+	0.505657i	$0.831250\pi$
$594$		0			0
$595$	2058.00	+	1782.28i	0.141798	+	0.122801i
$596$		0			0
$597$	−11686.5	−	20241.6i	−0.801167	−	1.38766i
$598$		0			0
$599$	−5140.50	+	8903.61i	−0.350643	+	0.607331i	−0.986362	−	0.164589i	$-0.947370\pi$
$599$	−5140.50	+	8903.61i	−0.350643	+	0.607331i	0.635719	+	0.771920i	$0.280704\pi$
$600$		0			0
$601$	−6090.00			−0.413338			−0.206669	−	0.978411i	$-0.566262\pi$
$601$	−6090.00			−0.413338			−0.206669	+	0.978411i	$0.566262\pi$
$602$		0			0
$603$	−9130.00			−0.616588
$604$		0			0
$605$	4571.00	−	7917.20i	0.307170	−	0.532033i
$606$		0			0
$607$	2474.50	+	4285.96i	0.165464	+	0.286593i	0.936820	−	0.349812i	$-0.113754\pi$
$607$	2474.50	+	4285.96i	0.165464	+	0.286593i	−0.771356	+	0.636404i	$0.780421\pi$
$608$		0			0
$609$	−7105.00	+	2461.24i	−0.472757	+	0.163768i
$610$		0			0
$611$	−3675.00	−	6365.29i	−0.243330	−	0.421460i
$612$		0			0
$613$	7898.50	−	13680.6i	0.520420	−	0.901394i	−0.479298	−	0.877652i	$-0.659109\pi$
$613$	7898.50	−	13680.6i	0.520420	−	0.901394i	0.999718	−	0.0237416i	$-0.00755791\pi$
$614$		0			0
$615$	−17150.0			−1.12448
$616$		0			0
$617$	−9378.00			−0.611903			−0.305951	−	0.952047i	$-0.598975\pi$
$617$	−9378.00			−0.611903			−0.305951	+	0.952047i	$0.598975\pi$
$618$		0			0
$619$	−12176.5	+	21090.3i	−0.790654	+	1.36945i	0.134908	+	0.990858i	$0.456926\pi$
$619$	−12176.5	+	21090.3i	−0.790654	+	1.36945i	−0.925562	+	0.378595i	$0.876407\pi$
$620$		0			0
$621$	−2782.50	−	4819.43i	−0.179803	−	0.311429i
$622$		0			0
$623$	1151.50	−	5983.37i	0.0740512	−	0.384781i
$624$		0			0
$625$	174.500	+	302.243i	0.0111680	+	0.0193435i
$626$		0			0
$627$	−857.500	+	1485.23i	−0.0546176	+	0.0946005i
$628$		0			0
$629$	−4599.00			−0.291533
$630$		0			0
$631$	12640.0			0.797449			0.398725	−	0.917071i	$-0.369453\pi$
$631$	12640.0			0.797449			0.398725	+	0.917071i	$0.369453\pi$
$632$		0			0
$633$	−6230.00	+	10790.7i	−0.391185	+	0.677553i
$634$		0			0
$635$	252.000	+	436.477i	0.0157485	+	0.0272772i
$636$		0			0
$637$	−686.000	−	4752.75i	−0.0426692	−	0.295621i
$638$		0			0
$639$	−4752.00	−	8230.71i	−0.294188	−	0.509549i
$640$		0			0
$641$	520.500	−	901.532i	0.0320726	−	0.0555513i	−0.849544	−	0.527518i	$-0.823123\pi$
$641$	520.500	−	901.532i	0.0320726	−	0.0555513i	0.881616	+	0.471967i	$0.156456\pi$
$642$		0			0
$643$	−9548.00			−0.585593			−0.292797	−	0.956175i	$-0.594586\pi$
$643$	−9548.00			−0.585593			−0.292797	+	0.956175i	$0.594586\pi$
$644$		0			0
$645$	−6076.00			−0.370918
$646$		0			0
$647$	−1620.50	+	2806.79i	−0.0984674	+	0.170551i	−0.911050	−	0.412295i	$-0.864727\pi$
$647$	−1620.50	+	2806.79i	−0.0984674	+	0.170551i	0.812583	+	0.582845i	$0.198061\pi$
$648$		0			0
$649$	−262.500	−	454.663i	−0.0158768	−	0.0274994i
$650$		0			0
$651$	−3601.50	+	18713.9i	−0.216826	+	1.12666i
$652$		0			0
$653$	4426.50	+	7666.92i	0.265272	+	0.459464i	0.967635	−	0.252355i	$-0.0812051\pi$
$653$	4426.50	+	7666.92i	0.265272	+	0.459464i	−0.702363	+	0.711819i	$0.747872\pi$
$654$		0			0
$655$	7521.50	−	13027.6i	0.448686	−	0.777147i
$656$		0			0
$657$	−24486.0			−1.45402
$658$		0			0
$659$	−7044.00			−0.416381			−0.208191	−	0.978088i	$-0.566757\pi$
$659$	−7044.00			−0.416381			−0.208191	+	0.978088i	$0.566757\pi$
$660$		0			0
$661$	6044.50	−	10469.4i	0.355679	−	0.616054i	−0.631555	−	0.775331i	$-0.717583\pi$
$661$	6044.50	−	10469.4i	0.355679	−	0.616054i	0.987234	+	0.159277i	$0.0509163\pi$
$662$		0			0
$663$	1029.00	+	1782.28i	0.0602761	+	0.104401i
$664$		0			0
$665$	−6002.50	+	2079.33i	−0.350026	+	0.121252i
$666$		0			0
$667$	−4611.00	−	7986.49i	−0.267674	−	0.463625i
$668$		0			0
$669$	4900.00	−	8487.05i	0.283176	−	0.490476i
$670$		0			0
$671$	−2065.00			−0.118805
$672$		0			0
$673$	982.000			0.0562456			0.0281228	−	0.999604i	$-0.491047\pi$
$673$	982.000			0.0562456			0.0281228	+	0.999604i	$0.491047\pi$
$674$		0			0
$675$	1330.00	−	2303.63i	0.0758396	−	0.131358i
$676$		0			0
$677$	15256.5	+	26425.0i	0.866108	+	1.50014i	0.865943	+	0.500143i	$0.166719\pi$
$677$	15256.5	+	26425.0i	0.866108	+	1.50014i	0.000164659		1.00000i	$0.499948\pi$
$678$		0			0
$679$	12348.0	+	10693.7i	0.697898	+	0.604397i
$680$		0			0
$681$	7717.50	+	13367.1i	0.434266	+	0.752171i
$682$		0			0
$683$	5737.50	−	9937.64i	0.321434	−	0.556740i	−0.659350	−	0.751836i	$-0.729169\pi$
$683$	5737.50	−	9937.64i	0.321434	−	0.556740i	0.980784	+	0.195096i	$0.0625019\pi$
$684$		0			0
$685$	−7875.00			−0.439253
$686$		0			0
$687$	−2009.00			−0.111569
$688$		0			0
$689$	2121.00	−	3673.68i	0.117277	−	0.203129i
$690$		0			0
$691$	−14157.5	−	24521.5i	−0.779416	−	1.34999i	−0.932279	−	0.361741i	$-0.882182\pi$
$691$	−14157.5	−	24521.5i	−0.779416	−	1.34999i	0.152862	−	0.988248i	$-0.451151\pi$
$692$		0			0
$693$	−1540.00	−	1333.68i	−0.0844152	−	0.0731057i
$694$		0			0
$695$	882.000	+	1527.67i	0.0481384	+	0.0833781i
$696$		0			0
$697$	3675.00	−	6365.29i	0.199714	−	0.345915i
$698$		0			0
$699$	−32109.0			−1.73744
$700$		0			0
$701$	10614.0			0.571876			0.285938	−	0.958248i	$-0.407695\pi$
$701$	10614.0			0.571876			0.285938	+	0.958248i	$0.407695\pi$
$702$		0			0
$703$	5365.50	−	9293.32i	0.287857	−	0.498583i
$704$		0			0
$705$	−12862.5	−	22278.5i	−0.687134	−	1.19015i
$706$		0			0
$707$	24132.5	−	8359.74i	1.28373	−	0.444697i
$708$		0			0
$709$	−5149.50	−	8919.20i	−0.272769	−	0.472451i	0.696801	−	0.717265i	$-0.254606\pi$
$709$	−5149.50	−	8919.20i	−0.272769	−	0.472451i	−0.969570	+	0.244814i	$0.921273\pi$
$710$		0			0
$711$	−1133.00	+	1962.41i	−0.0597621	+	0.103511i
$712$		0			0
$713$	−23373.0			−1.22767
$714$		0			0
$715$	−490.000			−0.0256293
$716$		0			0
$717$	−5838.00	+	10111.7i	−0.304078	+	0.526679i
$718$		0			0
$719$	16264.5	+	28170.9i	0.843621	+	1.46119i	0.886813	+	0.462128i	$0.152914\pi$
$719$	16264.5	+	28170.9i	0.843621	+	1.46119i	−0.0431924	+	0.999067i	$0.513753\pi$
$720$		0			0
$721$	−2376.50	+	12348.7i	−0.122754	+	0.637847i
$722$		0			0
$723$	−11931.5	−	20666.0i	−0.613744	−	1.06304i
$724$		0			0
$725$	2204.00	−	3817.44i	0.112903	−	0.195553i
$726$		0			0
$727$	−29456.0			−1.50270			−0.751350	−	0.659904i	$-0.770597\pi$
$727$	−29456.0			−1.50270			−0.751350	+	0.659904i	$0.770597\pi$
$728$		0			0
$729$	−11843.0			−0.601687
$730$		0			0
$731$	1302.00	−	2255.13i	0.0658772	−	0.114103i
$732$		0			0
$733$	−13933.5	−	24133.5i	−0.702109	−	1.21609i	−0.967725	−	0.252009i	$-0.918909\pi$
$733$	−13933.5	−	24133.5i	−0.702109	−	1.21609i	0.265616	−	0.964079i	$-0.414425\pi$
$734$		0			0
$735$	−2401.00	−	16634.6i	−0.120493	−	0.834799i
$736$		0			0
$737$	1037.50	+	1797.00i	0.0518546	+	0.0898147i
$738$		0			0
$739$	9769.50	−	16921.3i	0.486302	−	0.842299i	−0.513574	−	0.858045i	$-0.671679\pi$
$739$	9769.50	−	16921.3i	0.486302	−	0.842299i	0.999876	+	0.0157460i	$0.00501231\pi$
$740$		0			0
$741$	−4802.00			−0.238065
$742$		0			0
$743$	−1248.00			−0.0616214			−0.0308107	−	0.999525i	$-0.509809\pi$
$743$	−1248.00			−0.0616214			−0.0308107	+	0.999525i	$0.509809\pi$
$744$		0			0
$745$	703.500	−	1218.50i	0.0345963	−	0.0599226i
$746$		0			0
$747$	12012.0	+	20805.4i	0.588348	+	1.01905i
$748$		0			0
$749$	1599.50	−	8311.25i	0.0780300	−	0.405456i
$750$		0			0
$751$	14046.5	+	24329.3i	0.682509	+	1.18214i	0.974213	+	0.225631i	$0.0724444\pi$
$751$	14046.5	+	24329.3i	0.682509	+	1.18214i	−0.291704	+	0.956509i	$0.594222\pi$
$752$		0			0
$753$	16660.0	−	28856.0i	0.806274	−	1.39651i
$754$		0			0
$755$	−11333.0			−0.546292
$756$		0			0
$757$	35954.0			1.72625			0.863124	−	0.504991i	$-0.168504\pi$
$757$	35954.0			1.72625			0.863124	+	0.504991i	$0.168504\pi$
$758$		0			0
$759$	2782.50	−	4819.43i	0.133068	−	0.230480i
$760$		0			0
$761$	430.500	+	745.648i	0.0205067	+	0.0355187i	0.876097	−	0.482136i	$-0.160139\pi$
$761$	430.500	+	745.648i	0.0205067	+	0.0355187i	−0.855590	+	0.517654i	$0.826805\pi$
$762$		0			0
$763$	−19687.5	+	6819.95i	−0.934122	+	0.323589i
$764$		0			0
$765$	1617.00	+	2800.73i	0.0764219	+	0.132367i
$766$		0			0
$767$	735.000	−	1273.06i	0.0346014	−	0.0599315i
$768$		0			0
$769$	24710.0			1.15873			0.579366	−	0.815067i	$-0.303300\pi$
$769$	24710.0			1.15873			0.579366	+	0.815067i	$0.303300\pi$
$770$		0			0
$771$	5635.00			0.263216
$772$		0			0
$773$	−8249.50	+	14288.6i	−0.383847	+	0.664843i	−0.991609	−	0.129277i	$-0.958734\pi$
$773$	−8249.50	+	14288.6i	−0.383847	+	0.664843i	0.607761	+	0.794120i	$0.292068\pi$
$774$		0			0
$775$	−5586.00	−	9675.24i	−0.258910	−	0.448445i
$776$		0			0
$777$	21462.0	+	18586.6i	0.990920	+	0.858162i
$778$		0			0
$779$	8575.00	+	14852.3i	0.394392	+	0.683107i
$780$		0			0
$781$	−1080.00	+	1870.61i	−0.0494820	+	0.0857053i
$782$		0			0
$783$	2030.00			0.0926517
$784$		0			0
$785$	4753.00			0.216104
$786$		0			0
$787$	8235.50	−	14264.3i	0.373016	−	0.646083i	−0.617012	−	0.786954i	$-0.711657\pi$
$787$	8235.50	−	14264.3i	0.373016	−	0.646083i	0.990028	+	0.140871i	$0.0449902\pi$
$788$		0			0
$789$	899.500	+	1557.98i	0.0405869	+	0.0702985i
$790$		0			0
$791$	21532.0	+	18647.3i	0.967876	+	0.838205i
$792$		0			0
$793$	−2891.00	−	5007.36i	−0.129461	−	0.224233i
$794$		0			0
$795$	7423.50	−	12857.9i	0.331175	−	0.573613i
$796$		0			0
$797$	−36470.0			−1.62087			−0.810435	−	0.585828i	$-0.800769\pi$
$797$	−36470.0			−1.62087			−0.810435	+	0.585828i	$0.800769\pi$
$798$		0			0
$799$	11025.0			0.488156
$800$		0			0
$801$	3619.00	−	6268.29i	0.159639	−	0.276503i
$802$		0			0
$803$	2782.50	+	4819.43i	0.122282	+	0.211798i
$804$		0			0
$805$	19477.5	−	6747.20i	0.852785	−	0.295413i
$806$		0			0
$807$	12568.5	+	21769.3i	0.548243	+	0.949585i
$808$		0			0
$809$	−17875.5	+	30961.3i	−0.776847	+	1.34554i	0.156904	+	0.987614i	$0.449849\pi$
$809$	−17875.5	+	30961.3i	−0.776847	+	1.34554i	−0.933751	+	0.357924i	$0.883485\pi$
$810$		0			0
$811$	16492.0			0.714072			0.357036	−	0.934091i	$-0.383787\pi$
$811$	16492.0			0.714072			0.357036	+	0.934091i	$0.383787\pi$
$812$		0			0
$813$	9751.00			0.420643
$814$		0			0
$815$	−1634.50	+	2831.04i	−0.0702504	+	0.121677i
$816$		0			0
$817$	3038.00	+	5261.97i	0.130093	+	0.225328i
$818$		0			0
$819$	1078.00	−	5601.45i	0.0459931	−	0.238987i
$820$		0			0
$821$	20736.5	+	35916.7i	0.881497	+	1.52680i	0.849677	+	0.527304i	$0.176797\pi$
$821$	20736.5	+	35916.7i	0.881497	+	1.52680i	0.0318198	+	0.999494i	$0.489870\pi$
$822$		0			0
$823$	−12532.5	+	21706.9i	−0.530809	+	0.919387i	0.468545	+	0.883440i	$0.344778\pi$
$823$	−12532.5	+	21706.9i	−0.530809	+	0.919387i	−0.999354	+	0.0359479i	$0.988555\pi$
$824$		0			0
$825$	2660.00			0.112254
$826$		0			0
$827$	−9732.00			−0.409208			−0.204604	−	0.978845i	$-0.565591\pi$
$827$	−9732.00			−0.409208			−0.204604	+	0.978845i	$0.565591\pi$
$828$		0			0
$829$	−13877.5	+	24036.5i	−0.581406	+	1.00702i	0.413907	+	0.910319i	$0.364164\pi$
$829$	−13877.5	+	24036.5i	−0.581406	+	1.00702i	−0.995313	+	0.0967055i	$0.969170\pi$
$830$		0			0
$831$	1452.50	+	2515.80i	0.0606338	+	0.105021i
$832$		0			0
$833$	6688.50	+	2673.42i	0.278203	+	0.111199i
$834$		0			0
$835$	4214.00	+	7298.86i	0.174648	+	0.302500i
$836$		0			0
$837$	2572.50	−	4455.70i	0.106235	−	0.184004i
$838$		0			0
$839$	−21112.0			−0.868733			−0.434367	−	0.900736i	$-0.643028\pi$
$839$	−21112.0			−0.868733			−0.434367	+	0.900736i	$0.643028\pi$
$840$		0			0
$841$	−21025.0			−0.862069
$842$		0			0
$843$	−17339.0	+	30032.0i	−0.708407	+	1.22700i
$844$		0			0
$845$	7003.50	+	12130.4i	0.285122	+	0.493845i
$846$		0			0
$847$	4571.00	−	23751.6i	0.185433	−	0.963536i
$848$		0			0
$849$	14969.5	+	25927.9i	0.605126	+	1.04811i
$850$		0			0
$851$	−17410.5	+	30155.9i	−0.701321	+	1.21472i
$852$		0			0
$853$	−21238.0			−0.852492			−0.426246	−	0.904607i	$-0.640164\pi$
$853$	−21238.0			−0.852492			−0.426246	+	0.904607i	$0.640164\pi$
$854$		0			0
$855$	−7546.00			−0.301834
$856$		0			0
$857$	17804.5	−	30838.3i	0.709673	−	1.22919i	−0.255305	−	0.966861i	$-0.582176\pi$
$857$	17804.5	−	30838.3i	0.709673	−	1.22919i	0.964978	−	0.262330i	$-0.0844908\pi$
$858$		0			0
$859$	1088.50	+	1885.34i	0.0432353	+	0.0748858i	0.886833	−	0.462090i	$-0.152900\pi$
$859$	1088.50	+	1885.34i	0.0432353	+	0.0748858i	−0.843598	+	0.536975i	$0.819567\pi$
$860$		0			0
$861$	−42875.0	+	14852.3i	−1.69707	+	0.587882i
$862$		0			0
$863$	−16123.5	−	27926.7i	−0.635980	−	1.10155i	−0.986307	−	0.164921i	$-0.947263\pi$
$863$	−16123.5	−	27926.7i	−0.635980	−	1.10155i	0.350327	−	0.936627i	$-0.386070\pi$
$864$		0			0
$865$	9873.50	−	17101.4i	0.388103	−	0.672214i
$866$		0			0
$867$	31304.0			1.22623
$868$		0			0
$869$	515.000			0.0201038
$870$		0			0
$871$	−2905.00	+	5031.61i	−0.113011	+	0.195740i
$872$		0			0
$873$	9702.00	+	16804.4i	0.376132	+	0.651479i
$874$		0			0
$875$	19698.0	+	17059.0i	0.761045	+	0.659084i
$876$		0			0
$877$	−13815.5	−	23929.1i	−0.531946	−	0.921357i	−0.999305	−	0.0372891i	$-0.988128\pi$
$877$	−13815.5	−	23929.1i	−0.531946	−	0.921357i	0.467359	−	0.884068i	$-0.345206\pi$
$878$		0			0
$879$	27097.0	−	46933.4i	1.03977	−	1.80094i
$880$		0			0
$881$	24402.0			0.933172			0.466586	−	0.884476i	$-0.345484\pi$
$881$	24402.0			0.933172			0.466586	+	0.884476i	$0.345484\pi$
$882$		0			0
$883$	19612.0			0.747448			0.373724	−	0.927540i	$-0.378081\pi$
$883$	19612.0			0.747448			0.373724	+	0.927540i	$0.378081\pi$
$884$		0			0
$885$	2572.50	−	4455.70i	0.0977103	−	0.169239i
$886$		0			0
$887$	1130.50	+	1958.08i	0.0427942	+	0.0741218i	0.886629	−	0.462481i	$-0.153041\pi$
$887$	1130.50	+	1958.08i	0.0427942	+	0.0741218i	−0.843835	+	0.536603i	$0.819707\pi$
$888$		0			0
$889$	1008.00	+	872.954i	0.0380284	+	0.0329335i
$890$		0			0
$891$	2097.50	+	3632.98i	0.0788652	+	0.136599i
$892$		0			0
$893$	−12862.5	+	22278.5i	−0.482001	+	0.834851i
$894$		0			0
$895$	22771.0			0.850448
$896$		0			0
$897$	15582.0			0.580009
$898$		0			0
$899$	4263.00	−	7383.73i	0.158152	−	0.273928i
$900$		0			0
$901$	3181.50	+	5510.52i	0.117637	+	0.203754i
$902$		0			0
$903$	−15190.0	+	5261.97i	−0.559791	+	0.193917i
$904$		0			0
$905$	−5537.00	−	9590.37i	−0.203377	−	0.352259i
$906$		0			0
$907$	−11916.5	+	20640.0i	−0.436252	+	0.755611i	−0.997397	−	0.0721066i	$-0.977028\pi$
$907$	−11916.5	+	20640.0i	−0.436252	+	0.755611i	0.561145	+	0.827718i	$0.310361\pi$
$908$		0			0
$909$	30338.0			1.10698
$910$		0			0
$911$	−31824.0			−1.15738			−0.578692	−	0.815546i	$-0.696437\pi$
$911$	−31824.0			−1.15738			−0.578692	+	0.815546i	$0.696437\pi$
$912$		0			0
$913$	2730.00	−	4728.50i	0.0989593	−	0.171402i
$914$		0			0
$915$	−10118.5	−	17525.8i	−0.365582	−	0.633206i
$916$		0			0
$917$	7521.50	−	39082.9i	0.270863	−	1.40745i
$918$		0			0
$919$	−8409.50	−	14565.7i	−0.301854	−	0.522826i	0.674702	−	0.738090i	$-0.264272\pi$
$919$	−8409.50	−	14565.7i	−0.301854	−	0.522826i	−0.976556	+	0.215264i	$0.930939\pi$
$920$		0			0
$921$	25774.0	−	44641.9i	0.922130	−	1.59718i
$922$		0			0
$923$	−6048.00			−0.215680
$924$		0			0
$925$	−16644.0			−0.591623
$926$		0			0
$927$	−7469.00	+	12936.7i	−0.264632	+	0.458357i
$928$		0			0
$929$	−899.500	−	1557.98i	−0.0317671	−	0.0550222i	0.849705	−	0.527259i	$-0.176780\pi$
$929$	−899.500	−	1557.98i	−0.0317671	−	0.0550222i	−0.881472	+	0.472237i	$0.843447\pi$
$930$		0			0
$931$	−13205.5	+	10396.6i	−0.464869	+	0.365989i
$932$		0			0
$933$	−34912.5	−	60470.2i	−1.22506	−	2.12187i
$934$		0			0
$935$	367.500	−	636.529i	0.0128540	−	0.0222639i
$936$		0			0
$937$	14154.0			0.493480			0.246740	−	0.969082i	$-0.420641\pi$
$937$	14154.0			0.493480			0.246740	+	0.969082i	$0.420641\pi$
$938$		0			0
$939$	33271.0			1.15629
$940$		0			0
$941$	−6023.50	+	10433.0i	−0.208672	+	0.361431i	−0.951296	−	0.308277i	$-0.900247\pi$
$941$	−6023.50	+	10433.0i	−0.208672	+	0.361431i	0.742624	+	0.669708i	$0.233581\pi$
$942$		0			0
$943$	−27825.0	−	48194.3i	−0.960877	−	1.66429i
$944$		0			0
$945$	−857.500	+	4455.70i	−0.0295180	+	0.153380i
$946$		0			0
$947$	−12189.5	−	21112.8i	−0.418274	−	0.724472i	0.577492	−	0.816396i	$-0.304031\pi$
$947$	−12189.5	−	21112.8i	−0.418274	−	0.724472i	−0.995766	+	0.0919245i	$0.970698\pi$
$948$		0			0
$949$	−7791.00	+	13494.4i	−0.266498	+	0.461588i
$950$		0			0
$951$	24339.0			0.829912
$952$		0			0
$953$	−52330.0			−1.77874			−0.889368	−	0.457192i	$-0.848855\pi$
$953$	−52330.0			−1.77874			−0.889368	+	0.457192i	$0.848855\pi$
$954$		0			0
$955$	8949.50	−	15501.0i	0.303245	−	0.525236i
$956$		0			0
$957$	1015.00	+	1758.03i	0.0342845	+	0.0593825i
$958$		0			0
$959$	−19687.5	+	6819.95i	−0.662922	+	0.229643i
$960$		0			0
$961$	4091.00	+	7085.82i	0.137323	+	0.237851i
$962$		0			0
$963$	5027.00	−	8707.02i	0.168217	−	0.291360i
$964$		0			0
$965$	−2779.00			−0.0927038
$966$		0			0
$967$	12416.0			0.412897			0.206449	−	0.978457i	$-0.433809\pi$
$967$	12416.0			0.412897			0.206449	+	0.978457i	$0.433809\pi$
$968$		0			0
$969$	3601.50	−	6237.98i	0.119398	−	0.206804i
$970$		0			0
$971$	18406.5	+	31881.0i	0.608334	+	1.05367i	0.991515	+	0.129993i	$0.0414954\pi$
$971$	18406.5	+	31881.0i	0.608334	+	1.05367i	−0.383181	+	0.923673i	$0.625171\pi$
$972$		0			0
$973$	3528.00	+	3055.34i	0.116241	+	0.100668i
$974$		0			0
$975$	3724.00	+	6450.16i	0.122321	+	0.211867i
$976$		0			0
$977$	−17497.5	+	30306.6i	−0.572973	+	0.992418i	0.423286	+	0.905996i	$0.360877\pi$
$977$	−17497.5	+	30306.6i	−0.572973	+	0.992418i	−0.996259	+	0.0864221i	$0.972457\pi$
$978$		0			0
$979$	−1645.00			−0.0537022
$980$		0			0
$981$	−24750.0			−0.805511
$982$		0			0
$983$	−7150.50	+	12385.0i	−0.232010	+	0.401853i	−0.958399	−	0.285430i	$-0.907863\pi$
$983$	−7150.50	+	12385.0i	−0.232010	+	0.401853i	0.726390	+	0.687283i	$0.241197\pi$
$984$		0			0
$985$	−10199.0	−	17665.2i	−0.329916	−	0.571431i
$986$		0			0
$987$	−51450.0	−	44557.0i	−1.65924	−	1.43695i
$988$		0			0
$989$	−9858.00	−	17074.6i	−0.316953	−	0.548978i
$990$		0			0
$991$	−1332.50	+	2307.96i	−0.0427127	+	0.0739805i	−0.886591	−	0.462553i	$-0.846933\pi$
$991$	−1332.50	+	2307.96i	−0.0427127	+	0.0739805i	0.843879	+	0.536534i	$0.180267\pi$
$992$		0			0
$993$	23387.0			0.747396
$994$		0			0
$995$	−23373.0			−0.744697
$996$		0			0
$997$	−12435.5	+	21538.9i	−0.395021	+	0.684197i	−0.993104	−	0.117237i	$-0.962596\pi$
$997$	−12435.5	+	21538.9i	−0.395021	+	0.684197i	0.598083	+	0.801434i	$0.295929\pi$
$998$		0			0
$999$	−3832.50	−	6638.08i	−0.121376	−	0.210230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.4.i.c.81.1		2
4.3	odd	2		7.4.c.a.4.1	yes	2
7.2	even	3	inner	112.4.i.c.65.1		2
7.3	odd	6		784.4.a.r.1.1		1
7.4	even	3		784.4.a.b.1.1		1
8.3	odd	2		448.4.i.f.193.1		2
8.5	even	2		448.4.i.a.193.1		2
12.11	even	2		63.4.e.b.46.1		2
20.3	even	4		175.4.k.a.74.1		4
20.7	even	4		175.4.k.a.74.2		4
20.19	odd	2		175.4.e.a.151.1		2
28.3	even	6		49.4.a.c.1.1		1
28.11	odd	6		49.4.a.d.1.1		1
28.19	even	6		49.4.c.a.30.1		2
28.23	odd	6		7.4.c.a.2.1	✓	2
28.27	even	2		49.4.c.a.18.1		2
56.37	even	6		448.4.i.a.65.1		2
56.51	odd	6		448.4.i.f.65.1		2
84.11	even	6		441.4.a.d.1.1		1
84.23	even	6		63.4.e.b.37.1		2
84.47	odd	6		441.4.e.k.226.1		2
84.59	odd	6		441.4.a.e.1.1		1
84.83	odd	2		441.4.e.k.361.1		2
140.23	even	12		175.4.k.a.149.2		4
140.39	odd	6		1225.4.a.c.1.1		1
140.59	even	6		1225.4.a.d.1.1		1
140.79	odd	6		175.4.e.a.51.1		2
140.107	even	12		175.4.k.a.149.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.4.c.a.2.1	✓	2	28.23	odd	6
7.4.c.a.4.1	yes	2	4.3	odd	2
49.4.a.c.1.1		1	28.3	even	6
49.4.a.d.1.1		1	28.11	odd	6
49.4.c.a.18.1		2	28.27	even	2
49.4.c.a.30.1		2	28.19	even	6
63.4.e.b.37.1		2	84.23	even	6
63.4.e.b.46.1		2	12.11	even	2
112.4.i.c.65.1		2	7.2	even	3	inner
112.4.i.c.81.1		2	1.1	even	1	trivial
175.4.e.a.51.1		2	140.79	odd	6
175.4.e.a.151.1		2	20.19	odd	2
175.4.k.a.74.1		4	20.3	even	4
175.4.k.a.74.2		4	20.7	even	4
175.4.k.a.149.1		4	140.107	even	12
175.4.k.a.149.2		4	140.23	even	12
441.4.a.d.1.1		1	84.11	even	6
441.4.a.e.1.1		1	84.59	odd	6
441.4.e.k.226.1		2	84.47	odd	6
441.4.e.k.361.1		2	84.83	odd	2
448.4.i.a.65.1		2	56.37	even	6
448.4.i.a.193.1		2	8.5	even	2
448.4.i.f.65.1		2	56.51	odd	6
448.4.i.f.193.1		2	8.3	odd	2
784.4.a.b.1.1		1	7.4	even	3
784.4.a.r.1.1		1	7.3	odd	6
1225.4.a.c.1.1		1	140.39	odd	6
1225.4.a.d.1.1		1	140.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	112.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.50000 - 6.06218i) q^{3} +(-3.50000 - 6.06218i) q^{5} +(-14.0000 - 12.1244i) q^{7} +(-11.0000 - 19.0526i) q^{9} +(-2.50000 + 4.33013i) q^{11} -14.0000 q^{13} -49.0000 q^{15} +(10.5000 - 18.1865i) q^{17} +(24.5000 + 42.4352i) q^{19} +(-122.500 + 42.4352i) q^{21} +(-79.5000 - 137.698i) q^{23} +(38.0000 - 65.8179i) q^{25} +35.0000 q^{27} +58.0000 q^{29} +(73.5000 - 127.306i) q^{31} +(17.5000 + 30.3109i) q^{33} +(-24.5000 + 127.306i) q^{35} +(-109.500 - 189.660i) q^{37} +(-49.0000 + 84.8705i) q^{39} +350.000 q^{41} +124.000 q^{43} +(-77.0000 + 133.368i) q^{45} +(262.500 + 454.663i) q^{47} +(49.0000 + 339.482i) q^{49} +(-73.5000 - 127.306i) q^{51} +(-151.500 + 262.406i) q^{53} +35.0000 q^{55} +343.000 q^{57} +(-52.5000 + 90.9327i) q^{59} +(206.500 + 357.668i) q^{61} +(-77.0000 + 400.104i) q^{63} +(49.0000 + 84.8705i) q^{65} +(207.500 - 359.401i) q^{67} -1113.00 q^{69} +432.000 q^{71} +(556.500 - 963.886i) q^{73} +(-266.000 - 460.726i) q^{75} +(87.5000 - 30.3109i) q^{77} +(-51.5000 - 89.2006i) q^{79} +(419.500 - 726.595i) q^{81} -1092.00 q^{83} -147.000 q^{85} +(203.000 - 351.606i) q^{87} +(164.500 + 284.922i) q^{89} +(196.000 + 169.741i) q^{91} +(-514.500 - 891.140i) q^{93} +(171.500 - 297.047i) q^{95} -882.000 q^{97} +110.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 7 q^{3} - 7 q^{5} - 28 q^{7} - 22 q^{9} - 5 q^{11} - 28 q^{13} - 98 q^{15} + 21 q^{17} + 49 q^{19} - 245 q^{21} - 159 q^{23} + 76 q^{25} + 70 q^{27} + 116 q^{29} + 147 q^{31} + 35 q^{33} - 49 q^{35}+ \cdots + 220 q^{99}+O(q^{100}) \) 2 * q + 7 * q^3 - 7 * q^5 - 28 * q^7 - 22 * q^9 - 5 * q^11 - 28 * q^13 - 98 * q^15 + 21 * q^17 + 49 * q^19 - 245 * q^21 - 159 * q^23 + 76 * q^25 + 70 * q^27 + 116 * q^29 + 147 * q^31 + 35 * q^33 - 49 * q^35 - 219 * q^37 - 98 * q^39 + 700 * q^41 + 248 * q^43 - 154 * q^45 + 525 * q^47 + 98 * q^49 - 147 * q^51 - 303 * q^53 + 70 * q^55 + 686 * q^57 - 105 * q^59 + 413 * q^61 - 154 * q^63 + 98 * q^65 + 415 * q^67 - 2226 * q^69 + 864 * q^71 + 1113 * q^73 - 532 * q^75 + 175 * q^77 - 103 * q^79 + 839 * q^81 - 2184 * q^83 - 294 * q^85 + 406 * q^87 + 329 * q^89 + 392 * q^91 - 1029 * q^93 + 343 * q^95 - 1764 * q^97 + 220 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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